AP EAMCET · Maths · Mathematical Induction
If \(2^{\mathrm{n}}\) divides 16 ! and \(2^{\mathrm{n}+1}\) does not divide 16 !, then \(\mathrm{n}=\)
- A 14
- B 15
- C 16
- D 17
Answer & Solution
Correct Answer
(B) 15
Step-by-step Solution
Detailed explanation
Since \(2^n\) divides 16 ! and \(2^{n+1}\) does not divide 16 !. \(\therefore n=\) Number of times 2 occurs in \(16 !\) \(=\left[\frac{16}{2}\right]+\left[\frac{16}{2^2}\right]+\left[\frac{16}{2^3}\right]+\left[\frac{16}{2^4}\right]=8+4+2+1=15\)
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